Help yourself

In 1966 Kac asked the question "Can one hear the shape of a drum?",
i.e. do the frequencies of a drum's vibration fully determine its
shape? For plane domains with fixed boundary (which are the closest
to the physical drums), this question was answered in the negative by
Gordon, Webb and Wolpert (GWW) in 1992. Their construction based on
the so-called Sunada method (1984) that uses representation theory.
Various proofs, generalizations and applications of this construction
exist; in particular one recent application is in the study of Dirac
points in the spectrum of graphene, by A.Comech and myself. The above
link illustrates a proof (due to Chapman) of the GWW example using
foldable paper models.

CRM school "Geometric and Computational Spectral Theory"

This is a class file containing routines for setting up a quantum
graph, computing its eigenvalue and computing and plotting its
eigenfunctions. It was developed basing on the code by Phuongmai Truong
and Ram Band with the primary aim of aiding in understanding the
behavior of the zeros of the eigenfunctions.